NASHVILLE, Tenn. -- With the Astros having added a starting pitcher late Tuesday in the trade that brought Alex White over from the Rockies in exchange for reliever Wilton Lopez, it appears the club will leave the Winter Meetings without any other significant news outside of the Rule 5 Draft.

General manager Jeff Luhnow said his top goal during his stay in the Music City was acquiring a designated hitter in advance of the team's move to the American League in 2013, but he's content to let some other chips fall before adding a bat to increase run production.

"We're not necessarily concerned about leaving Nashville with a DH in place," Luhnow said Wednesday. "I think we've got a long time between now and Opening Day, so we'll definitely have an opportunity to fill that spot."

Luhnow said the Astros aren't very close to any deals.

"We're comfortable with where we are," he said. "There are a few things we're working on that are hypothetical we would pursue, but they don't appear to be very close at this point. "

Luhnow told reporters he met with representatives from Moye Sports Associates, which represents Lance Berkman, as well as Josh Hamilton, though the Astros aren't players in the Hamilton sweepstakes. Luhnow has made clear his interest in bringing Berkman back to Houston as the DH.

"We had a discussion with them and had a very basic conversation," he said. "We haven't talked anything specifically at this point."

Luhnow would like to meet face-to-face with Berkman at some point later this month to find out how his rehab is going and how he's feeling. Berkman hit .301 with 31 homers and 94 RBIs for St. Louis in 2011, but he was limited to 81 at-bats last season because of knee injuries.

"We'll probably take that as an opportunity to see if there's mutual interest," Luhnow said.

Berkman reached out to Astros owner Jim Crane last month for a face-to-face meeting and also had lunch with manager Bo Porter. Berkman lives in Houston and plans to become a volunteer assistant at Rice University if he decides to retire.

As far as where Berkman ranks on the team's wish list, Luhnow wouldn't say.

"There is some interest, and I'll leave it at that," he said. "It all depends on how the rest of our team is configured. It depends on a few other factors. I can't tell you where the option of attempting to sign Lance ranks relative to others, because there are some different paths we're considering simultaneously."

The Astros have the first pick in Thursday morning's Rule 5 Draft and appear to have settled on a player to take. Clubs pay $50,000 to select a player, and he has to stay on the 25-man roster for the full season or be offered back to his former team for $25,000.

"It's a big commitment to take someone and tell your manager this is a player you need to keep on the 25-man all year," Luhnow said. "We did it to two guys last year [pitcher Rhiner Cruz and shortstop Marwin Gonzalez] and they both made it through, but to do another one or two this year, it has be the right type of player that fits a need, because if it's just taking your roster and shrinking it to 24, you're putting your manager at a disadvantage. You have to have your manager on board."

Luhnow didn't rule out taking two players on Thursday.

"It depends on who else is selected after we make our first selection," he said. "There are other players on our list, but if they're not there we will probably pass the second round."